# 经济代写|微观经济学代写Microeconomics代考|ECON20002

## 经济代写|微观经济学代写Microeconomics代考|LONG RUN VERSUS SHORT RUN

We will study the firm’s cost-minimization problem in the long run and in the short run. Although the terms long run and short run seem to connote a length of time, it is more useful to think of them as pertaining to the degree to which the firm faces constraints in its decision-making flexibility. A firm that makes a long run decision faces a blank slate (i.e., no constraints): Over the long run, it will be able to vary the quantities of all its inputs as much as it desires. When our sporting goods firm in the previous section decides whether to build a new bowling ball factory, it faces a long-run decision. It is free to choose whether to build the factory and, if so, how large to make it. As it does this, it can simultaneously choose other input quantities, such as the size of the workforce and the amount of land for the factory. Because the firm can, in principle, avoid the costs of all inputs by choosing not to build, the costs associated with this long-run decision are necessarily nonsunk.

By contrast, a firm facing a short-run decision is subject to constraints: Over the short run, it will not be able to adjust the quantities of some of its inputs and/or reverse the consequences of past decisions that it has made regarding those inputs. For example, once our bowling ball firm builds a factory, it will, at least for a while, face short-run decisions, such as how many workers it should employ given the physical constraints of its capacity.

In microeconomics, the concept of short run and long run is convenient analytical simplifications to help us focus our attention on the interesting features of the problem at hand. In reality, firms face a continuum of “runs”; some decisions involve “blanker slates” than others. In this section, we first focus on long-run cost minimization in order to study carefully the trade-offs that firms can make in input choices when they start with a blank slate. In the next section, we turn to short-run cost minimization to highlight how constraints on input usage can limit the firm’s ability to minimize costs.

## 经济代写|微观经济学代写Microeconomics代考|THE LONG-RUN COST-MINIMIZATION PROBLEM

The cost-minimization problem is an example of constrained optimization, first discussed in Chapter 1. We want to minimize the firm’s total costs, subject to the requirement that the firm produce a given amount of output. In Chapter 4, we encountered two other examples of constrained optimization: the problem of maximizing utility subject to a budget constraint (utility maximization) and the problem of minimizing consumption expenditures, subject to achieving a minimum level of utility (expenditure minimization). You will see that the cost-minimization problem closely resembles the expenditure-minimization problem from consumer choice theory.

Let’s study the long-run cost-minimization problem for a firm that uses two inputs: labor and capital. Each input has a price. The price of a unit of labor servicesalso called the wage rate-is $w$. This price per unit of capital services is $r$. The price of labor could be either an explicit cost or an implicit cost. It would be an explicit cost if the firm (as most firms do) hires workers in the open market. It would be an implicit cost if the firm’s owner provides her own labor to run the firm and, in so doing, sacrifices outside employment opportunities. Similarly, the price of capital could either be an explicit cost or an implicit cost. It would be an explicit cost if the firm leased capital services from another firm (e.g., a firm that leases computer time on a server to host its website). It would be an implicit cost if the firm owned the physical capital and, by using it in its own business, sacrificed the opportunity to sell capital services to other firms.

The firm has decided to produce $Q_0$ units of output during the next year. In later chapters, we will study how the firm makes such an output decision. For now, the quantity $Q_0$ is exogenous (e.g., as if the manufacturing manager of the firm has been told how much to produce). The long-run cost-minimization problem facing the manufacturing manager is to figure out how to produce that amount in the cost-minimizing way. Thus, the manager must choose a quantity of capital $K$ and a quantity of labor $L$ that minimize the total cost $T C=w L+r K$ of producing $Q_0$ units of output. This total cost is the sum of all the economic costs the firm incurs when it uses labor and capital services to produce output.

# 微观经济学代考

## 经济代写|微观经济学代写Microeconomics代考|THE LONG-RUN COST-MINIMIZATION PROBLEM

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